Write a number in every square so that each region of joined, equal numbers has exactly that many squares.
The full guide, with a worked example and common mistakes: How to play Number Regions.
Yes — there can be many regions of 3, as long as no two of them touch along a side.
Yes — every puzzle here is checked to have exactly one solution.
It sets the largest region in the puzzle, which also keeps puzzles a sensible size to solve.
Open the Number Regions Solver, type the numbers and press Solve.